#ifndef SEEN_Geom_POINT_H
#define SEEN_Geom_POINT_H

/**
 *  \file
 *  \brief Defines a Cartesian 2D Point class.
 */

#include <iostream>

#include "coord.h"
#include "utils.h"

namespace Geom {
    
    enum Dim2 { X=0, Y=1 };
    
    class Matrix;
    
    /// Cartesian 2D point.
    class Point {
        Coord _pt[2];
        
    public:
        inline Point()
        { _pt[X] = _pt[Y] = 0; }
        
        inline Point(Coord x, Coord y) {
            _pt[X] = x; _pt[Y] = y;
        }
        
        inline Point(Point const &p) {
            for (unsigned i = 0; i < 2; ++i)
                _pt[i] = p._pt[i];
        }
        
        inline Point &operator=(Point const &p) {
            for (unsigned i = 0; i < 2; ++i)
                _pt[i] = p._pt[i];
            return *this;
        }
        
        inline Coord operator[](unsigned i) const { return _pt[i]; }
        inline Coord &operator[](unsigned i) { return _pt[i]; }
        
        Coord operator[](Dim2 d) const throw() { return _pt[d]; }
        Coord &operator[](Dim2 d) throw() { return _pt[d]; }
        
        static inline Point polar(Coord angle, Coord radius) {
            return Point(radius * std::cos(angle), radius * std::sin(angle));
        }
        
        inline Coord length() const { return hypot(_pt[0], _pt[1]); }
        
        /** Return a point like this point but rotated -90 degrees.
         (If the y axis grows downwards and the x axis grows to the
         right, then this is 90 degrees counter-clockwise.)
         **/
        Point ccw() const {
            return Point(_pt[Y], -_pt[X]);
        }
        
        /** Return a point like this point but rotated +90 degrees.
         (If the y axis grows downwards and the x axis grows to the
         right, then this is 90 degrees clockwise.)
         **/
        Point cw() const {
            return Point(-_pt[Y], _pt[X]);
        }
        
        /**
         \brief A function to lower the precision of the point
         \param  places  The number of decimal places that should be in
         the final number.
         */
        inline void round (int places = 0) {
            _pt[X] = (Coord)(decimal_round((double)_pt[X], places));
            _pt[Y] = (Coord)(decimal_round((double)_pt[Y], places));
            return;
        }
        
        void normalize();
        
        inline Point operator+(Point const &o) const {
            return Point(_pt[X] + o._pt[X], _pt[Y] + o._pt[Y]);
        }
        inline Point operator-(Point const &o) const {
            return Point(_pt[X] - o._pt[X], _pt[Y] - o._pt[Y]);
        }
        inline Point &operator+=(Point const &o) {
            for ( unsigned i = 0 ; i < 2 ; ++i ) {
                _pt[i] += o._pt[i];
            }
            return *this;
        }
        inline Point &operator-=(Point const &o) {
            for ( unsigned i = 0 ; i < 2 ; ++i ) {
                _pt[i] -= o._pt[i];
            }
            return *this;
        }
        
        inline Point operator-() const {
            return Point(-_pt[X], -_pt[Y]);
        }
        inline Point operator*(double const s) const {
            return Point(_pt[X] * s, _pt[Y] * s);
        }
        inline Point operator/(double const s) const {
            //TODO: s == 0?
            return Point(_pt[X] / s, _pt[Y] / s);
        }
        inline Point &operator*=(double const s) {
            for ( unsigned i = 0 ; i < 2 ; ++i ) _pt[i] *= s;
            return *this;
        }
        inline Point &operator/=(double const s) {
            //TODO: s == 0?
            for ( unsigned i = 0 ; i < 2 ; ++i ) _pt[i] /= s;
            return *this;
        }
        
        Point &operator*=(Matrix const &m);
        
        inline int operator == (const Point &in_pnt) {
            return ((_pt[X] == in_pnt[X]) && (_pt[Y] == in_pnt[Y]));
        }
        
        friend inline std::ostream &operator<< (std::ostream &out_file, const Geom::Point &in_pnt);
    };
    
    inline Point operator*(double const s, Point const &p) { return p * s; }
    
    /** A function to print out the Point.  It just prints out the coords
     on the given output stream */
    inline std::ostream &operator<< (std::ostream &out_file, const Geom::Point &in_pnt) {
        out_file << "X: " << in_pnt[X] << "  Y: " << in_pnt[Y];
        return out_file;
    }
    
    /** This is a rotation (sort of). */
    inline Point operator^(Point const &a, Point const &b) {
        Point const ret(a[0] * b[0] - a[1] * b[1],
                        a[1] * b[0] + a[0] * b[1]);
        return ret;
    }
    
    //IMPL: boost::EqualityComparableConcept
    inline bool operator==(Point const &a, Point const &b) {
        return (a[X] == b[X]) && (a[Y] == b[Y]);
    }
    inline bool operator!=(Point const &a, Point const &b) {
        return (a[X] != b[X]) || (a[Y] != b[Y]);
    }
    
    /** This is a lexicographical ordering for points.  It is remarkably useful for sweepline algorithms*/
    inline bool operator<=(Point const &a, Point const &b) {
        return ( ( a[Y] < b[Y] ) ||
                (( a[Y] == b[Y] ) && ( a[X] < b[X] )));
    }
    
    Coord L1(Point const &p);
    
    /** Compute the L2, or euclidean, norm of \a p. */
    inline Coord L2(Point const &p) { return p.length(); }
    
    /** Compute the square of L2 norm of \a p. Warning: this can overflow where L2 won't.*/
    inline Coord L2sq(Point const &p) { return p[0]*p[0] + p[1]*p[1]; }
    
    double LInfty(Point const &p);
    bool is_zero(Point const &p);
    bool is_unit_vector(Point const &p);
    
    extern double atan2(Point const p);
    /** compute the angle turning from a to b (signed). */
    extern double angle_between(Point const a, Point const b);
    
    //IMPL: NearConcept
    inline bool are_near(Point const &a, Point const &b, double const eps=EPSILON) {
        return ( are_near(a[X],b[X],eps) && are_near(a[Y],b[Y],eps) );
    }
    
    inline
    Point middle_point(Point const& P1, Point const& P2)
    {
        return (P1 + P2) / 2;
    }
    
    /** Returns p * Geom::rotate_degrees(90), but more efficient.
     *
     * Angle direction in Inkscape code: If you use the traditional mathematics convention that y
     * increases upwards, then positive angles are anticlockwise as per the mathematics convention.  If
     * you take the common non-mathematical convention that y increases downwards, then positive angles
     * are clockwise, as is common outside of mathematics.
     *
     * There is no rot_neg90 function: use -rot90(p) instead.
     */
    inline Point rot90(Point const &p) { return Point(-p[Y], p[X]); }
    
    /** Given two points and a parameter t \in [0, 1], return a point
     * proportionally from a to b by t.  Akin to 1 degree bezier.*/
    inline Point lerp(double const t, Point const a, Point const b) { return (a * (1 - t) + b * t); }
    
    Point unit_vector(Point const &a);
    
    /** compute the dot product (inner product) between the vectors a and b. */
    inline Coord dot(Point const &a, Point const &b) { return a[0] * b[0] + a[1] * b[1]; }
    /** Defined as dot(a, b.cw()). */
    inline Coord cross(Point const &a, Point const &b) { return dot(a, b.cw()); }
    
    /** compute the euclidean distance between points a and b.  TODO: hypot safer/faster? */
    inline Coord distance (Point const &a, Point const &b) { return L2(a - b); }
    
    /** compute the square of the distance between points a and b. */
    inline Coord distanceSq (Point const &a, Point const &b) { return L2sq(a - b); }
    
    Point abs(Point const &b);
    
    Point operator*(Point const &v, Matrix const &m);
    
    Point operator/(Point const &p, Matrix const &m);
    
} /* namespace Geom */

#endif /* !SEEN_Geom_POINT_H */

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